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Proof step 26 from proof validrefs-contains-null (previous step)

refs0 = [], st[r -- i '] = refval(r0), acc + jvmref ' = r0 ' + refs, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, acc + jvmref ' + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), ∀ str, refs0, ty, st. validrefs(str, acc + jvmref ' + refs0, ty, st) → validrefs(str, r0 ' + refs, ty, st) ∧ refs0 = [] ⊦ r = jvmref, ¬ r0 ∈ acc ∧ r0 ≠ jvmref, jvmref ≠ r0 ∧ ¬ jvmref ∈ refs, (∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval ∧ validrefs(str, st[r -- i0 '] .refval ' + refs, st[r -- _type] .type .type, st)) ∧ refs0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
acc + jvmref ' = r0 ' + refs, st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, ∀ str, refs0, ty, st. validrefs(str, acc + jvmref ' + refs0, ty, st) → validrefs(str, r0 ' + refs, ty, st) ∧ refs0 = [] ⊦ r = jvmref, jvmref ≠ r0 ∧ ¬ jvmref ∈ refs, ¬ r0 ∈ acc ∧ r0 ≠ jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs])]]